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Topic: Lorenz curve

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	Definitions Country Codes geographic.org Courty Profiles - Flags, Maps, Economy, Geography, Climate, Natural ...
		The index is calculated from the Lorenz curve, in which cumulative family income is plotted against the number of families arranged from the poorest to the richest.
		The index is the ratio of (a) the area between a country's Lorenz curve and the 45 degree helping line to (b) the entire triangular area under the 45 degree line.
		If income were distributed with perfect equality, the Lorenz curve would coincide with the 45 degree line and the index would be zero; if income were distributed with perfect inequality, the Lorenz curve would coincide with the horizontal axis and the right vertical axis and the index would be 100.
	www.theodora.com /wfb/wfb2000/definitions.html (12538 words)

	LORENZ CURVE
		Lorenz curve was developed by Max O. Lorenz in order to describe the extent of inequality in a society.
		The Lorenz curve is a graphical representation of the proportionality of a distribution (the cumulative percentage of the values).
		The Gini coefficient is defined graphically as a ratio of two surfaces involving the summation of all vertical deviations between the Lorenz curve and the perfect equality line (A) divided by the difference between the perfect equality and perfect inequality lines (A+B).
	sociologyindex.com /lorenz_curve.htm (420 words)

	Lorenz curve - Wikipedia, the free encyclopedia
		The Lorenz curve is a graphical representation of the cumulative distribution function of a probability distribution; it is a graph showing the proportion of the distribution assumed by the bottom y% of the values.
		The Gini coefficient is the area between the line of perfect equality and the observed Lorenz curve, as a percentage of the area between the line of perfect equality and the line of perfect inequality.
		The Lorenz curve for a probability distribution is a continuous function.
	en.wikipedia.org /wiki/Lorenz_curve (961 words)

	Technical Notes
		Lorenz curves are an effective way of showing inequality of income within and between countries (see Figure 1).
		The closer the Lorenz curve of a region is to the 45-degree line the more equal the distribution of income is. In the case of the Lorenz curve in the diagram above 20% of the population earns 5% of the income and 50% of the population earns 20% of the income.
		The more the Lorenz curve bends away from the 45-degree line of absolute equality, the less equal is the distribution of income.
	www.nscb.gov.ph /ru10/teknotes/tnidi.htm (655 words)

	Search ScienceWorld
		The Lorenz curve is a function of the cumulative proportion of ordered individuals mapped onto the corresponding cumulative proportion of their size.
		The Lorenz asymmetry coefficient is defined as S=F(mu)+L(mu), where the functions F and L are defined as for the Lorenz curve.
		The Gini coefficient (or Gini ratio) G is a summary statistic of the Lorenz curve and a measure of inequality in a population.
	scienceworld.wolfram.com /search/index.cgi?num=&q=Lorenz+History (344 words)

	Measures of Inequality
		Lorenz curve is an important tool for the analysis of inequality in a variety of situations – inequality in the distribution of income within a population, inequality in the productivity of scientists in a give population, inequality in the allocation of research grants to different institutions by a funding agency, etc.
		When all the members of the population receive the same income, the Lorenz curve is the equidistribution or identity function F = L.
		Gini coefficient is twice the area between the Lorenz curve and the equidistribution function.
	www.unesco.org /webworld/idams/advguide/Chapt3_1_4.htm (206 words)

	[No title]
		The Gini coefficient is based on the Lorenz curve, that is a cumulative frequency curve that compares the empirical distribution of a variable with its uniform distribution (based on equality), represented by a diagonal line.
		The concentration curve and concentration index are calculated by the same method as the Lorenz curve and the Gini coefficient, but incorporating the social dimension.
		The Lorenz curve and the Gini coefficient take full advantage of the information on all subjects or population groups but their disadvantage is that they overlook socioeconomic status.
	www.paho.org /english/dd/ais/be_v26n2-en-desigualdades_3.htm (2021 words)

	Lorenz Curve -- from Wolfram MathWorld
		The Lorenz curve is used in economics and ecology to describe inequality in wealth or size.
		The total amount of inequality can be summarized by the Gini coefficient (also called the Gini ratio), which is the ratio between the area enclosed by the line of equality and the Lorenz curve, and the total triangular area under the line of equality.
		The degree of asymmetry around the axis of symmetry is measured by the so-called Lorenz asymmetry coefficient.
	mathworld.wolfram.com /LorenzCurve.html (251 words)

	[No title]
		This equality distribution is represented by a diagonal line, and the greater the deviation of the Lorenz curve from this line, the greater the inequality.
		Graph the curve using the X axis for the proportion of the cumulative population (live births) and the Y axis for the proportion of cumulative health variable observations (infant deaths).
		Lorenz Curve: For example, we read on the graph that 30% of infant deaths occur among 20% of the population of live births.
	www.paho.org /English/SHA/be_v22n1-Gini.htm (985 words)

	The Lorenz Curve for Income Distribution (Site not responding. Last check: )
		The Lorenz curve is a graphical way of representing the income distribution of a population.
		The Gini Coefficient for a Lorenz curve is defined as the ratio of the area between the Lorenz curve and the diagonal to the triangle below the diagonal line.
		In the graph below the area between the Lorenz curve and the diagonal is shown in green.
	www2.sjsu.edu /faculty/watkins/lorenz.htm (277 words)

	bp_casefair_econf_7e\|Income Distribution and Poverty\|The Distribution of Income\|Income Inequality in the United ...
		To graph a Lorenz curve, the percentage of households is placed on the horizontal axis and the percentage of total income is found on the vertical axis.
		The Gini coefficient is the area between the Lorenz curve and the 45-degree line, divided by the whole area under the 45-degree line.
		A perfectly unequal income distribution is when one person has 100% of the wealth; thus, the Lorenz curve is the horizontal axis until the last person is reached, and the Gini coefficient is 1.
	wps.prenhall.com /bp_casefair_econf_7e/0,8233,2031471-,00.html (394 words)

	Appendix: The Lorenz curve
		The Lorenz curve is a graphical device used to demonstrate the equity of distribution of a given variable such as income, asset ownership or wealth.
		The principles outlined in the derivation of the curve can be applied to any data set in which the equity of distribution for a given variable is being calculated.
		This plotted curve is then compared with the line of perfect equity (drawn at 45° from the origin of the graph) to provide an indication of the equity of distribution of cattle holdings within the area concerned.
	www.fao.org /Wairdocs/ILRI/x5547E/x5547e0l.htm (856 words)

	Lorenz curve - Encyclopedia.com
		Lorenz curve A graph which is used in the study of social stratification in order to show the extent to which the actual distribution of a particular good (usually income, earnings, or wealth) deviates from a condition of perfect equality.
		The nearer the curve is towards the line of complete equality, the more equal the distribution; the nearer it is towards the rectangular boundary, the more unequal the distribution.
		In the figure shown, for example, the curves suggest that the degree of income inequality was greater at time i that an time ii.
	www.encyclopedia.com /doc/1O88-Lorenzcurve.html (658 words)

	NetLogo Models Library: Wealth Distribution
		For a numerical measurement of the inequity in the distribution of wealth, the Gini index (or Gini coefficient) is derived from the Lorenz curve.
		If, however, the Lorenz curve is a backwards "L", then the Gini-Index would be 1 -- the area between the Lorenz curve and the 45 degree line is 0.5; this quantity divided by 0.5 is 1.
		The LORENZ CURVE plot shows the Lorenz curve of the population at a particular time as well as the 45 degree line of equality.
	www.ccl.sesp.northwestern.edu /netlogo/models/WealthDistribution (1526 words)

	Gini Project
		The area under the curve is given by an integral but we do not have a formula for the curve, we just have a few data points.
		The estimate for the area under the Lorenz curve using left endpoints, the left sum, is
		The Gini index is defined as the area between the diagonal line y=x and the Lorenz curve y=f(x) (the shaded area in the figure below).
	www.cord.edu /faculty/andersod/gini_web.html (704 words)

	A Dollar a Day :: Measuring Poverty I (Site not responding. Last check: )
		A Lorenz curve graphs the share (in percentile form) of the total income the bottom x% of the population receive, ranging from 0% to 100%.
		To determine the Gini coefficient using this data, a ratio of the regions formed by a Lorenz curve is used.
		For example, if the area of the region between the line of equality and the Lorenz curve is called A (represented in red on the sample graph) and the area of the region between the curve and graph’s bounds is called B (represented in blue on the sample graph), then the Gini-coefficient would be A/(A+B).
	library.thinkquest.org /05aug/00282/over_measure1.htm (1308 words)

	[No title] (Site not responding. Last check: )
		If the Lorenz curve is the 45 degree line then the Gini index would be 0; there is no area between the Lorenz curve and the 45 degree line.
		the Lorenz curve is a backwards "L", then the Gini-Index would be 1 -- the area between the Lorenz curve and the 45 degree line is 0.5; this quantity divided by 0.5 is 1.
		The Gini coefficient is calculated as a ratio of the areas on the Lorenz curve diagram.
	www.lycos.com /info/gini-coefficient.html (664 words)

	Lorenz Asymmetry Coefficient -- from Wolfram MathWorld
		The Lorenz asymmetry coefficient is a summary statistic of the Lorenz curve that measures the degree of asymmetry of a Lorenz curve.
		, then the point where the Lorenz curve is parallel with the line of equality is above the axis of symmetry.
		, then the point where the Lorenz curve is parallel to the line of equality is below the axis of symmetry.
	mathworld.wolfram.com /LorenzAsymmetryCoefficient.html (131 words)

	The Lorenz Curve
		If the curve in one case is farther away from the line of perfect equality for every value along the horizontal axis, then that case is considered to have less equality than a case with a curve nearer to the equality line.
		However, Lorenz curves representing discontinuous functions can be constructed as the limit of Lorenz curves of probability distributions, the line of perfect inequality being an example.
		Lorenz curves can be used to look at a distribution of a single year, or the changes in the Lorenz curve over time can by analyzed.
	www.urbansim.org /docs/tutorials/lorenz-curve/node2.html (354 words)

	WIID
		A straightforward graphical interpretation of the Gini coefficient is the Lorenz curve, which is the thick curve in the figure above.
		In the case of a completely egalitarian income distribution in which the whole population has equal incomes, the Lorenz curve would be the dashed straight 45-degree line.
		The Gini coefficient is the area A between the 45-degree line and the Lorenz curve divided by 1/2, the total area under the 45-degree line.
	www.wider.unu.edu /wiid/ginieq.htm (664 words)

	Estimating Lorenz curves using a Dirichlet distribution. \| Accounting from AllBusiness.com
		The Lorenz curve relates the cumulative proportion of income to the cumulative proportion of population.
		When a particular functional form of the Lorenz curve is specified, it is typically estimated by linear or nonlinear least squares estimation techniques that have good properties when the error terms are independently and normally distributed.
		The Lorenz curve is one of the most important tools upon which the measurement of income inequality is based.
	www.allbusiness.com /accounting/134196-1.html (822 words)

	CSISS Classics - John Kirtland Wright: Early Quantitative Geography, 1937
		The Lorenz Curve takes social variables, such as population, income, voting patterns, crime, or land area and compares them with one another to find the relative evenness of distribution in space.
		Wright believed that the Lorenz Curve would be a valuable analytical tool for looking at topics such as the spread of the population between the largest U.S. cities or the distribution of rainfall in different parts of the country, which indeed it was.
		In later decades, use of the Lorenz Curve increased, becoming a political tool during the desegregation efforts of the 1960s and 1970s and later for studying issues such as health care access and environmental racism.
	www.csiss.org /classics/content/11 (620 words)

	Distribution and Lorenz Functions (statistics)
		To determine Lorenz function break points, the ordered data vector is cumulated, and at each step the cumulated total is divided by the grand total.
		The Lorenz function plotted against the proportion of the ordered population gives a Lorenz curve, which is always contained in the lower triangle of the unit square.
		The Gini coefficient represents twice the area between the Lorenz function and the diagonal plotted in the unit square.
	www.unesco.org /webworld/idams/Doc/ManualHtml/E2quanti.htm (633 words)

	nthd.org (Site not responding. Last check: )
		I ported over the Cinema4d COFFEE script that generated a Lorenz Curve to MEL.
		The Lorenz Curve is one of the classic symbols of complexity theory, its unpredictable yet coherent behavior is complex in apprearnce - but easy to create.
		Lorenz Curve Screenshot This script will generate a Lorenz Curve based on "N" number of iterations.
	www.nthd.org /nthd/209 (199 words)

	SSRN-Asymptotically Distribution-Free Statistical Test for Generalized Lorenz Curves: An Alternative Approach by Kuan Xu
		A generalized Lorenz (GL) curve differs from a Lorenz curve in that the former is a rescaled version of the latter.
		A GL curve represents the relationship between the average income computed from a cumulative percentage of the population and the corresponding cumulative percentage.
		Relative to a dominated GL curve, a dominating GL curve indicates both that total income for the population is higher and that it is more equally distributed.
	papers.ssrn.com /sol3/papers.cfm?abstract_id=142932 (282 words)

	[No title]
		These factors have let to higher wages for skilled workers by shifting the demand curve for skilled workers to the right and to lower wages for unskilled workers by shifting the demand curve for unskilled workers to the left (and perhaps by shifting the supply curve for unskilled labor to the right).
		The area under the Lorenz curve for: the 20th percentile is ½(0.20)(0.07) = 0.007.
		Recall that the area under the Lorenz Curve for Country A is 0.24.
	www.mtsu.edu /~cbaum/442topic7.doc (3594 words)

	Visualizing
		The Lorenz curve is the dark red curve in Figure 8 above.
		As a result, the Lorenz curve for an equal distribution would be a forty-five degree diagonal line, shown by the green line in Figure 8.
		The curvature of the Lorenz curve, as it droops below the 45 degree line, shows the inequality of the income distribution.
	william-king.www.drexel.edu /top/prin/txt/factors/dist3.html (229 words)

	5th UK user meeting abstract
		The well-known Lorenz curve for a variable y plots L(p(y)) against p(y) where p(y) is the cumulative distribution function of y and L(p(y)) is the cumulative share of y up to p(y) (i.e.
		The generalised Lorenz curve, is the Lorenz curve with y-ordinates multiplied by the mean of y.
		The interest of generalised Lorenz curves comparisons will be emphasised and the simple data transformations needed to obtain related structures will also be illustrated.
	www.stata.com /meeting/5uk/glcurve.html (233 words)

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